58 Mr. A. R. McLeod on the 



Substituting in the formula (19) and (29), we have the- 

 values of the lags in the mean temperature of the bulbs 

 which are given below. The temperatures are in degrees 

 centigrade, the times in seconds, and Vj is large so that the 

 inversion occurs only when the steady lag on the first gra- 

 dient has been attained. If t<t^ we write t' — in the two 

 formulse. The two gradients used, viz. : G=*028° C./sec, 

 and G' = '185° C./sec , correspond to temperature gradients 

 of l°-68 C. and 11°-10 C. per thousand feet of height (5°'5 0. 

 and 36' 7° 0. per km,), and a rate of climb of 1000 feet per 

 minute. In the case of a cylindrical bulb, the length need 

 only be sufficient to enable the effects of the ends to be 

 neglected. Formula (19) is then applicable. 



Mercury Spliere. 



When G--028 the steady lag is 1°"21 C. 

 G' = -185 „ „ „ „ 8°-00C. 



(i.) When G = '028 and G'=- '185, 



L 1= -8-00-6-22 e- 0231t + 9*22 e -' 0231t '. . (31) 



(ii.) When G= -'028 and G'=-fl85, 



Lo = 8-00-3-79--° 23K -9-22e- 023 "'. . . . (32) 



(iii.) When G=-'028 and G'= +-028, 



L3 = l-21-3-79 6- 023U -2-42^- 0231f . . . (33) 



Curves are plotted in fig. 1, the straight lines representing 

 true temperatures. 



Alcohol Sphere. 



When G='028 the steady lag is 1°'29 C. 



„ G--185 „ „ „ „ 8°'57C. 



The lags in the three cases considered above are : 



L x = -8*57-5-57 e- 0192 ^--54e--° 8 ^--ll^-- 205r 

 + 9-59 e- 0l92t ' + '26 e" out ' + '02 *-***', 



(34) 



L 2 =8'57-3-06e--° 192 ^ 



(3o) 



- 9*59 e --° l92t '-'2Q e - (JMt '-'02 e~- 2m \ I 



■=1-29 -3-06 e - 0l92t -'4,7 e- 08it -'lle-' 2(] 

 -2-52 e -° im '-'07 e~' mt -'01 e ~ ,2m '. 



(36) 



